Hit-and-run mixes fast

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It is shown that the "hit-and-run" algorithm for sampling from a convex body K (introduced by R.L. Smith) mixes in time O*(n2R2/r2), where R and r are the radii of the inscribed and circumscribed balls of K. Thus after appropriate preprocessing, hit-and-run produces an approximately uniformly distributed sample point in time O*(n3), which matches the best known bound for other sampling algorithms. We show that the bound is best possible in terms of R, r and n.

Original languageEnglish
Pages (from-to)443-461
Number of pages19
JournalMathematical Programming, Series B
Issue number3
Publication statusPublished - Dec 1999


ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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